Edge Imbalance Sequences and Their Graphicness: [preprint]
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Date
2019
Authors
Kozerenko, Sergiy
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Abstract
The main focus of combinatorial dynamics is put on the structure of periodic
points (and the corresponding orbits) of topological dynamical systems. The
first result in this area is the famous Sharkovsky’s theorem which completely
describes the coexistence of periods of periodic points for a continuous map
from the closed unit interval to itself. One feature of this theorem is that it
can be proved using digraphs of a special type (the so-called periodic graphs).
In this paper we use Markov graphs (which are the natural generalization of
periodic graphs in case of dynamical systems on trees) as a tool to study several
classes of maps on trees. The emphasis is put on linear and metric maps.
Description
Keywords
Markov graphs, Sharkovsky’s theorem, maps on trees, article, preprint
Citation
Kozerenko S. Edge Imbalance Sequences and Their Graphicness / Kozerenko Sergiy // Journal of Advanced Mathematical Studies. - 2019. - Vol. 12, No. 1. - P. 50-62.